[expert { circle problem }] ........

Geometry Level 2

For each natural number k , let Ck denote the circle with radius k centimetres and the centre at origin . On the circle Ck , a particle moves k centimetres in the counter clockwise direction . After completing its motion on Ck , the particle moves to C(k+1) in the radial direction . the motion of the particle continues in this manner . The particle starts at (1,0) if the particle crosses the positive direction of x -axis for the first time on the circle Cn, then n =

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